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中文摘要：
对一种新形状变幅杆进行了研究.根据刚体定轴转动的理论,推导得出变截面杆扭转振动方程,通过对反比例函数的优化,求出解析解.利用边界条件求出变幅杆的各项参数（放大倍数、谐振长度、频率方程以及输入阻抗）,并对输入阻抗随频率的变化进行研究.最后利用有限元软件Ansys对超声变幅杆扭转振动进行模拟.结果表明：共振频率的模态分析值与理论分析结果一致,这为变幅杆设计提供了依据.
英文摘要：
In this work,a new kind of shape horn is studied.Based on the theory of fixed-axis rotation of rigid body,the torsional vibration equation of variable cross-section is established.By optimizing the inverse proportion function,the analytical solution of ultrasonic horn is obtained.According to the boundary conditions,the various parameters of ultrasonic horn,such as the magnification,resonance length,and the input impedance are derived.Finally,the model of ultrasonic horn′s torsional vibration is simulated by using the finite element software ANSYS,the results of resonance frequency modal are consistent with that of the theoretical value.
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